[" Define "f(x)={[x^(2)+bx+c,,x<1],[x,,x>=1]" if "f(x)],[" is differentiable at "x=1," then "(b-c)=]

Define f(x)={{:(x^2+bx+c,","xlt1),(x,","xge1):} } .If f(x) is differentiable at x=1 , then (b-c)=

Define f(x) = {{:(x^(2)+bx+c , ",",x lt 1),(x,",",x ge 1):} . If f(x) is differentiable at x = 1, then (b - c) =

Define f(x) = {{:(x^(2)+bx+c , ",",x lt 1),(x,",",x ge 1):} . If f(x) is differentiable at x = 1 , then (b - c) =

If f(x) ={{:( (a cos x+bx sin x+ce^(x)-2x)/(x^(2)), xne 0),( 0, x=0):} is differentiable at x=0 , then (a) a+b+c=2 (b) a+b=-4 (c) f'(0)=1/3 (d) a-c=4

A function f is defined as f(x)={:{[(1)/(|x|)" if "|x|>=(1)/(2)],[a+bx^(2)" if "|x|<(1)/(2)]:} if f(x) is derivable at x=(1)/(2) then a-b=

If f(x)=x^2 and is differentiable an [1,2] f'(c) at c where c in [1,2]:

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

f(x)={ax^(2)+bx+c,|x|>1x+1,|x|<=1 If f(x) is continuous for all values of x, then;